Well-posedness theorems in fluid-structure interaction: perfectly elastic shells
摘要
In this work, we consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell is perfectly elastic while the fluid is governed by the Navier--Stokes equations. Consequently, damping within the coupled system comes entirely from the parabolic fluid subsystem. Our main result is the construction of a local-in-time unique strong solution to the system of PDEs. Standard techniques from the literature do not apply here. They are restricted to visco-elastic structures, where the corresponding solid phase is parabolic. Our construction relies on a different method built upon a new estimate for the acceleration of the system. In the case of a 2D viscous incompressible fluid interacting with a 1D perfectly elastic shell we can extend the local solution globally in time (until a possible self-intersection of the shell).
引用
@article{arxiv.2605.14357,
title = {Well-posedness theorems in fluid-structure interaction: perfectly elastic shells},
author = {Dominic Breit and Prince Romeo Mensah and Sebastian Schwarzacher and Pei Su},
journal= {arXiv preprint arXiv:2605.14357},
year = {2026}
}